“This states that genetic risk factors act independently of each other, with each variant increasing genetic risk by the same amount regardless of what other risk factors are present*. Of course, this is clearly a spherical cow situation”

Which is precisely what you’d expect if the cows evolved to be spherical. Some of our DNA has clearly been modularized (i.e. selected specifically for a lack of polygenicity). It’s like an approximation of a local function (say, a bell curve) that consists of a discrete (but infinite) sum of frequencies (sinuosoids of some sort). A finite approximation will repeat eventually (periodicitypolygenicity), but an infinite (and non-repeating) one runs into all these silly “philosophical issues” when you try to apply it outside theoretical mathematics. Thankfully thermodynamics accounts for the fuzzyness and, lo, functional modularity exists (except perhaps in the eyes of a few naysayers).

Evidently this is not the entire story.

Justin Loe

Found something on the evolutionary implications of epistasis in populations:

http://www.ncbi.nlm.nih.gov/pubmed/19366665
Neher RA, Shraiman BI., Kavli Institute for Theoretical Physics, University of California, Santa Barbara
“We demonstrate that a large number of polymorphic interacting loci can, despite frequent recombination, exhibit cooperative behavior that locks alleles into favorable genotypes leading to a population consisting of a set of competing clones. …Our results demonstrate that the collective effect of many weak epistatic interactions can have dramatic effects on the population structure.”

Justin Loe

This appears to establish a potential upper bound on epistasis, assuming that the model is valid:

“”The attained ﬁtness is maximal at K = 3 to 5, from which we infer
that an intermediate amount of epistasis and pleiotropy is most
conducive to adaptation”

using the NK model:
“NK model of genetic interactions [31–33] consists of circular, binary
sequences encoding the alleles at N loci, where each locus contributes
to the ﬁtness of the haplotype via an interaction with K other loci.””

Justin Loe

duplicate post deleted by me

http://www.scribd.com/doc/74944514/ Robert Dole

Competition between recombination and epistasis can cause a transition from allele to genotype selection (2009)

“Standing variation harbored in natural population provides important raw material for selection to act upon, in particular after a sudden change in environments or hybridization events (20)”

Epistasis is pervasive in E.coli and S.cerevisiae. That is an experimental fact. On what theoretical basis would one think that the same is not true for H.sapiens?

http://www.scribd.com/doc/74944514/ Robert Dole

I was suggesting it was tentatively allied with pleiotropy and additivity in the human genome (which it is). A caveman graph is a discrete idealization of this balancing act. The fact that actual “cavemen” were supplying the outlier phenotypes just demonstrates that sometimes language has a mind of its own (e.g. “The French call it…pied de Néanderthal.“)

“One obvious candidate for the most highly clustered graph possible is the complete graph, in which every vertex is adjacent to every other vertex. However, this construction automatically violates the sparseness condition, as it necessarily has k = n — 1. What is required, then, is a graph that is globally sparse but locally dense. that is, with k << n and y ~ 1.

A better solution is what might be termed the caveman graph, which consists of a number of fully connected clusters (or "caves") in which every member is adjacent with every other (Fig. 4.1). Every vertex has degree ky and so each cluster must consist of n_local = k + 1 vertices, and there must be n_global = n/(k + 1) such clusters. Note also that all edges are part of multiple triads, so no edge is a shortcut. Hence the caveman graph satisfies the sparseness condition and still has y = 1, but it fails to satisfy another essential condition: that it be connected. The best solution, then, appears to be a close approximation to the caveman graph that is both periodic and connected.“

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About Razib Khan

I have degrees in biology and biochemistry, a passion for genetics, history, and philosophy, and shrimp is my favorite food. In relation to nationality I'm a American Northwesterner, in politics I'm a reactionary, and as for religion I have none (I'm an atheist). If you want to know more, see the links at http://www.razib.com